Stable Synchronous Propagation in Feedforward Networks for Biped Locomotion

TL;DR

This paper demonstrates how stable phase-synchronous signals can propagate along feedforward neural chains, applying this concept to biped locomotion using Wilson-Cowan neuron models and providing analytic stability conditions.

Contribution

It extends previous work on phase propagation stability to Wilson-Cowan neuron models and applies it to biped locomotion, offering analytic stability criteria and numerical insights.

Findings

Stable phase propagation is achievable in Wilson-Cowan models.

Analytic conditions for stability are derived for certain rate models.

Application to biped locomotion demonstrates practical relevance.

Abstract

Rhythmic gait patterns in animal locomotion are widely believed to be produced by a central pattern generator (CPG), a network of neurons that drives the muscle groups. In previous papers we have discussed how phase-synchronous signals can propagate along chains of neurons using a feedforward lift of the CPG, given sufficient conditions for stability to synchrony-breaking perturbations, and shown that stable signals are common for four standard neuron models. Here we apply these ideas to biped locomotion using a fifth model: Wilson-Cowan (or rate model) neurons. Feedforward architecture propagates the phase pattern of a CPG along a chain of identical modules. For certain rate models, we give analytic conditions that are sufficient for transverse Liapunov and Floquet stability. We compare different notions of transverse stability, summarise some numerical simulations, and outline an application to signal propagation in a model of biped locomotion.